The Model of the Integrated Control of Plant Pests with Natural Enemy

Abstract:

This paper mainly indicates the pest-control problem by using the biological control and the pesticide control. Firstly, it analyzed the continuous changing population of the three species-plants, plant pest and natural enemy-and the pesticides’ effects to establish a three-species model of the pests’ integrated control. Secondly, the pest equilibrium points with the natural enemy and that without natural enemy were obtained. We discussed the stability of the equilibrium points by the Hurwitz theorem and the first approximation method of stability and got the sufficient conditions for asymptotic stability. Finally, numerical simulations were performed by Matlab to analyze and verify the integrated control of plant pests in the situations with some natural enemies and without enemy. Moreover, the effects of spraying pesticides which have different killing rates on enemy and plant pest were analyzed.

• Periodical: Advanced Materials Research (Volumes 864-867)
• Pages: 2522-2527
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.864-867.2522
• Online since: December 2013
• Authors: Xu Ying Lv, Tian Wen Yao, Ding Jiang Wang*
• Keywords: Integrated Control, Plant Pests, Stability, Three Species

References

[1] Xinyu Song, Hongjian Guo, Xiangyun Shi, The theory of impulsive differential equations and its applications[M], Beijing: Science Press, 2011 (in Chinese).

[2] Diekmann, O., Heesterbeek, J.A.P.: Mathematical Epidemiology of Infectious Diseases[M]. Wiley, NewYork, (2000).

[3] Hyman, J.M., Li, J.: An intuitive formulation for the reproductive Number for the spread of diseases in heterogeneous populations[J]. Math. Biosci. 167, 65–86 (2000).

DOI: 10.1016/s0025-5564(00)00025-0

[4] May, R.M.: Stability and Complexity in Model Ecosystems. Monographs in Population Biology 6[M], Princeton University Press, Princeton, New Jersey, (1974).

[5] Dingjiang Wang, Research Development of Nonlinear Forest Evolution Systems[J], Journal of Biomathematics, 2008, 23(1): 125-131 (in Chinese).

[6] Xiao-xin Liao, Theory Methods and Application of Stability (2nd Edition)[M], Wuhan: H uazhong University of Science & Technology press, 2009. 10 (in Chinese).

[7] Qishao Lv, Linping Peng, Zhuoqin Yang, Ordinary Differential Equations and Dynamical Systems [M], Beijing: Beihang University Press, 2009. 5 (in Chinese).